Nonlinear Integral Evolution Equations Associated with a Riemann-Hilbert Scattering Problem. Aspects of the Initial Value Problem for the Sine-Hilbert Class

摘要

Results on a class of nonlinear evolution equations purely integral in space and solvable via the inverse scattering transform method are reviewed. The direct linearization for this class of equations is obtained together with a multisoliton solution. Properties of the linear problem, a matrix homogeneous Riemann-Hilbert boundary value problem, are obtained and aspects of the associated scattering theory are presented.